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       Wkh surri iru wklv frqvwudlqw uhgxfwlrq wkhruhp lv vwdqgdug dqg wkhuhiruh rplwwhg khuh1
       Vhfrqg0ehvw vxevlglhv duh fkdudfwhul}hg e|

                                                      v @ 3


dqg

                                                   ve @ t =


Ri frxuvh/ t  lv wkh dprxqw ri lqirupdwlrqdo uhqw h{wudfwhg e| wkh orz0frvw vhuylfh surylghu1


                                                           44
   Wkh djhqf|*v sd|r lv wkhuhiruh

                    A
                   Y +s> g,    s ^y+te ,  te e  t ` . +4  s, ^y+t ,  t  . g` =

+Vxevfulsw D ghqrwhv wkurxjkrxw wkh fdvh zkhuh wkh djhqf| ex|v dvvhwv/ l1h1 frqyhqwlrqdo sxeolf
vhuylfh surylvlrq1 Vxshuvfulsw W lqglfdwhv wuxwk0whoolqj1,
   Krzhyhu/ rqfh wkh gdpdjh frqwudfw zlwk wkh exloghu kdv ehhq vshflhg/ wklv wuxwk0whoolqj frq0
wudfw pd| qrw eh rswlpdo iurp wkh srlqw ri ylhz ri wkh djhqf|1 Iru odujh hqrxjk gdpdjh sd|phqwv/
wkh djhqf| pd| kdyh dq lqfhqwlyh wr lqgxfh wkh vhuylfh surylghu wr plvuhsuhvhqw frvw dv kljk dozd|v/
vr wkdw wkh djhqf| fdq h{wudfw gdpdjh sd|phqwv iurp wkh exloghu1 Zh vwxg| suhflvho| zkdw wklv
lqfhqwlyh lv ehorz1 Lq wkdw fdvh/ wkh rqo| elqglqj frqvwudlqwv rq wkh djhqf|*v pd{lpl}dwlrq sureohp
duh +7, dqg +8,1 Wkdw lv/ wkh djhqf| rhuv wkh vhuylfh surylghu vxevlglhv ve @ v @ 31 Wkh vhuylfh
surylghu wkhuhiruh uhsruwv kljk frvw + , dozd|v dqg lv uhlpexuvhg iru lwv ghfoduhg frvw t  1 Wklv
doorzv wkh djhqf| wr rewdlq gdpdjhv g dozd|v dqg lwv sd|r lv wkhuhiruh

                                          
                                         Y +g,       y+t ,  t  . g=

+Vxshuvfulsw P lqglfdwhv plvuhsuhvhqwdwlrq1,
   Iru frpsohwhqhvv/ zh eulh | vkrz wkdw wkh djhqf| zrxog qhyhu zdqw wr lpsohphqw d uhqhg
plvuhsuhvhqwdwlrq frqwudfw lq zklfk wkh vhuylfh surylghu plvuhsuhvhqwv wkh frvw dv ehlqj orz dozd|v1
Wklv lv irupdol}hg e| wkh iroorzlqj

Ohppd 5     Iru wkh jryhuqphqw djhqf|/ d uhqhg plvuhsuhvhqwdwlrq frqwudfw lq zklfk wkh vhuylfh

surylghu dozd|v uhsruwv kljk frvw grplqdwhv d uhqhg plvuhsuhvhqwdwlrq frqwudfw lq zklfk wkh vhuylfh

surylghu dozd|v uhsruwv orz frvw1


   Surri1   Zh qhhg wr suryh wkdw

                                 y+t ,  t   . g    y+te ,  tee  te =

+Zh suryh wklv e| vkrzlqj wkdw

                                    y+t ,  t     y+te ,  te e  te =

Vlqfh g  3/ wklv suryhv wkh ohppd1, Wklv lpsolhv/ dqg lv lpsolhg e|/

                                            y+te ,  y +t ,    t =

                                                         45
Glylglqj erwk vlghv e| t dqg wdnlqj olplwv dv t                      $ 3/ zh kdyh

                                                          y  +t ,     =

Uhfdoo wkdw y +t , @ t 3Q +t ,/ zklfk lv ohvv wkdq +ru htxdo wr,  iru doo ihdvleoh ydoxhv ri t 1
       Zh qrz wdnh d vwhs edfn wr vwxg| zklfk lqyhvwphqwv lq dvvhw txdolw| zloo eh lpsohphqwhg1
Lq rughu wr lqgxfh lqyhvwphqw e| wkh exloghu/ wkh djhqf| qhhgv wr vshfli| gdpdjhv lq wkh exlog
frqwudfw ri g     l/<   dqg lw qhhgv wr lpsohphqw wkh wuxwk0whoolqj frqwudfw zlwk wkh vhuylfh surylghu1
Li erwk frqglwlrqv duh vdwlvhg/ wkh djhqf|*v sd|r iurp wkh srlqw ri frqwudfwlqj zlwk wkh vhuylfh
                     A
surylghu iruzdug lv Y +sQ > g,/ dqg lqyhvwphqwv xs wr d frvw ri l                     g zloo eh pdgh e| wkh exloghu1
Li wkh djhqf| lpsohphqwv d uhqhg plvuhsuhvhqwdwlrq frqwudfw/ qr lqyhvwphqw zloo eh pdgh e| wkh
exloghu +zkr lv vxffhvvixoo| vxhg iru gdpdjhv lq hyhu| vwdwh ri qdwxuh,1 Iluvw/ zh kdyh wkh iroorzlqj

Ohppd 6         Li g @ 3/ wkh jryhuqphqw djhqf| suhihuv wkh uhqhg wuxwk0whoolqj frqwudfw wr d uhqhg

plvuhsuhvhqwdwlrq frqwudfw1


       Surri1   Zh qhhg wr suryh wkdw

                         s+y+te ,  te e    t , . +4  s,+y+t ,  t  ,  y+t ,  t  =

Zh wkhuhiruh qhhg wr vkrz wkdw

                                       y +te ,  te  e    t   y+t ,  t  =

Wklv lpsolhv/ dqg lv lpsolhg e|/

                                                 y +te ,  y+t ,       te =

Glylglqj erwk vlghv e| t dqg wdnlqj olplwv dv t                      $ 3/ zh kdyh

                                                          y +t ,     e =

Uhfdoo wkdw y +t , @ t 3Q +t ,/ zklfk lv juhdwhu wkdq +ru htxdo wr,  e iru doo ihdvleoh ydoxhv ri t 1
   <
    Vxssrvh wkdw lw lv nqrzq wkdw wkh wuxwk0whoolqj frqwudfw zlwk wkh vhuylfh surylghu zloo eh zulwwhq1 Wkh exloghu
nqrzv wkdw li vwdwh ri qdwxuh 5 rffxuv +wkh rqo| vwdwh ri qdwxuh lq zklfk wkh lqyhvwphqw lv uhohydqw, lpsohphqwlqj wkh
lqyhvwphqw zloo frvw  exw dyrlg gdpdjhv _1 Wkhuhiruh/ lw zloo lqyhvw zkhq _ 1   ,




                                                                46
                                                                            A             
   Dv wkh h{shfwhg gdpdjh sd|phqw g lqfuhdvhv iurp }hur/ vlqfh erwk sd|rv Y +s> g, dqg Y +g,
duh olqhdu lq g +exw lqfuhdvh dw glhuhqw udwhv,/ wkhuh h{lvwv vrph gW vxfk wkdw iru doo g ? gW /
 A                             A    
Y A Y / dqg iru doo g A gW / Y ? Y 1 Lq idfw/

                                        gW @ y +te ,  y+t ,  t e =

                  A               
   Frpsdulvrq ri Y +sQ > g, dqg Y +g, wkhuhiruh jlyhv xv rxu uvw uhvxow=

Sursrvlwlrq 7    Zkhq wkh jryhuqphqw djhqf| kdv sxufkdvhg dqg rzqv wkh dvvhw/ lqyhvwphqw fdq

eh lqgxfhg xs wr dq lqyhvwphqw frvw ri

                   l @ y+te ,  y +t , . t     te e  t  @ y+te ,  y+t ,  te=
   Surri1   Wkh sursrvlwlrq iroorzv iurp wkh dujxphqw lq wkh wh{w1
   Wkh sursrvlwlrq vwdwhv wkdw/ lq rughu wr lpsohphqw frvwo| lqyhvwphqwv/ frqwudfwxdoo| vshflhg
gdpdjh sd|phqwv pxvw eh kljk1 Krzhyhu/ jlyhq wkh exlog frqwudfw/ wkh djhqf| frxog kdyh dq
lqfhqwlyh wr frooxgh zlwk wkh vhuylfh surylghu wr h{wudfw gdpdjhv iurp wkh exloghu1 Wkh exloghu
nqrzv wklv dqg wkhuhiruh grhv qrw lqfxu wkh frvwo| lqyhvwphqw1
   Wkh kljkhvw ohyho ri gdpdjhv iru zklfk wkh lqfhqwlyh iru wkh djhqf| wr lpsohphqw wkh plvuhs0
uhvhqwdwlrq frqwudfw grhv qrw h{lvw lv

                                        gW @ y+te ,  y +t ,  te >

zklfk lv wkhuhiruh wkh prvw frvwo| lqyhvwphqw wkdw fdq eh lpsohphqwhg1 Zh phqwlrqhg wklv srvvl0
elolw| suhylrxvo|1 Iru frpsohwhqhvv/ zh kdyh qrz glvsrvhg ri wklv srvvlelolw|1
   Ixuwkhupruh/ zh duh deoh wr vkrz wkdw wkh djhqf| zrxog qhyhu zlvk wr lpsohphqw dq| lqyhvw0
phqwv wkdw duh pruh frvwo| wkdq gW hyhq li lw zhuh deoh wr gr vr e| vrphkrz suhyhqwlqj frooxvlrq1
Vxssrvh wkdw wkh djhqf| frxog frpplw wr qrw zulwlqj d plvuhsuhvhqwdwlrq frqwudfw1 Wkh djhqf|*v
h{ dqwh sd|r iurp zulwlqj wkh lqfhqwlyh frqwudfw wkdw lpsohphqwv lqyhvwphqw l +dqg wkhuhiruh d

exlog frqwudfw zlwk gdpdjhv ri vl}h g @ l lv qhfhvvdu|,/ lv

                                   Y +sQ > g,  +sQ
                                    A
                                                         sB,l  +4  sQ,g
+wkh exloghu qhhgv wr eh uhlpexuvhg iru lwv h{shfwhg lqyhvwphqw frvw/ dqg iru h{shfwhg gdpdjh
sd|phqwv,1 Wkh djhqf|*v h{ dqwh sd|r iurp zulwlqj dq lqfhqwlyh frqwudfw wkdw grhv qrw lpsohphqw
lqyhvwphqw +dqg wkhuhiruh uhtxluhv }hur gdpdjhv lq wkh exlog frqwudfw, lv

                   Y +sB > 3, @ sB ^y +te ,  te e
                    A
                                                        t ` . +4  sB , ^y+t ,  t  ` =

                                                        47
Frpsdulvrq ri wkhvh wzr sd|rv whoov xv wkdw wkh djhqf| qhyhu zlvkhv wr lpsohphqw lqyhvwphqwv
deryh

                   l @ y +te ,  y+t , . t     te e  t  @ y+te ,  y+t ,  te >

zklfk lv mxvw wkh vdph h{suhvvlrq dv wkdw ghulyhg deryh1


615     SxeolfSulydwh Sduwqhuvklsv

Wkh ihdwxuh ri wkh SSS prgho lv wkdw wkh djhqf| ex|v wkh vhuylfh dqg zulwhv d frqwudfw rq vhuylfh
surylvlrq rqo|1 Lq wklv iudphzrun/ wkh SIF dovr exlogv wkh dvvhw1 Wklv uhqhg frqwudfw lv wkh
vhfrqg0ehvw rswlpdo +wuxwkwhoolqj, frqwudfw1 Dv lv vwdqgdug/ wklv frqwudfw doorzv wkh SIF wr fdswxuh
lqirupdwlrq uhqw1 Wkh lqfhqwlyh wr lqyhvw lq h!flhqw dvvhwv lv wkhuhiruh ghwhuplqhg e| wkh lqfuhdvh
lq lqirupdwlrq uhqw iurp pdnlqj wkh lqyhvwphqw1 Wkh djhqf| fdq wkhuhiruh lpsohphqw uhodwlyho|
fkhds lqyhvwphqwv dw qr dgglwlrqdo frvw= wkh vwdqgdug lqirupdwlrq uhqw uhtxluhg wr lpsohphqw
wuxwk0whoolqj e| wkh SIF lv vx!flhqw wr lpsohphqw rswlpdo lqyhvwphqw dovr1 Wklv lv wkh vwdqgdug
dujxphqw iurp lqwhuqdol}dwlrq ri dq h{whuqdolw|1 Wkh pruh frvwo| lqyhvwphqwv duh/ krzhyhu/ wkh
pruh lqirupdwlrq uhqw wkh djhqf| qhhgv wr ohdyh wr wkh SIF lq rughu wr dfklhyh lqyhvwphqw1 Wkh
djhqf| lv zloolqj wr surylgh lqfhqwlyhv wr lpsohphqw h!flhqf| hqkdqflqj lqyhvwphqw xs wr wkh srlqw
zkhuh lqfuhdvlqj wkh lqirupdwlrq uhqw dq| ixuwkhu ehfrphv wrr frvwo|1
   Wkh SIF uhqhg frqwudfw lv d vwdqgdug frqwudfwlqj sureohp xqghu dgyhuvh vhohfwlrq1 Dv ehiruh/
zkhq wkh glvwulexwlrq ryhu  lv nqrzq wr eh i+e > s,> +  > +4  s,,j +zkhuh s fdq eh hlwkhu sB ru
sQ / ghshqglqj rq zkhwkhu wkh lqyhvwphqw zdv fduulhg rxw,/ wkh djhqf| ghvljqv d uhqhg frqwudfw

+vfkhgxoh ri vxevlglhv, ive > v j iru wkh SIF vr dv wr

                         pd{ s ^y+te ,  te e  ve ` . +4  s, ^y +t ,  t   v `          +9,
                         re cr


vxemhfw wr wkh xvxdo lqfhqwlyh frpsdwlelolw| dqg lqglylgxdo udwlrqdolw| frqvwudlqwv +5,+8,1 Djdlq/
ri frxuvh/ vhfrqg0ehvw vxevlglhv duh fkdudfwhul}hg e|

                                                       v @ 3


dqg

                                                    ve @ t =




                                                         48
       Wkh djhqf|*v sd|r jlyhq wkhvh vxevlglhv lv=

                          Y7 +s, @ s ^y+te ,  te e      t ` . +4  s, ^y+t ,  t  ` =

+Vxevfulsw V ghqrwhv wkh fdvh zkhuh wkh djhqf| ex|v vhuylfhv rqo|/ l1h1/ wkh SSS fdvh1,
       Vlqfh lq wklv vhwwlqj/ vxevlglhv +ru/ pruh suhflvho|/ wkh glhuhqfh ehwzhhq vxevlglhv iru wkh
orz0frvw surylghu w|sh dqg wkh kljk0frvw surylghu w|sh/ ve  v , jryhuq wkh lqfhqwlyh wr pdnh wkh
h!flhqf| hqkdqflqj lqyhvwphqw/ wkh djhqf| pd| qg lw rswlpdo wr lqfuhdvh ve eh|rqg ve @ t /
li wkh orvv iurp lqfuhdvhg uhqw lv rxwzhljkhg e| wkh jdlq lq dq lqfuhdvhg suredelolw| ri rewdlqlqj
dq h!flhqw dvvhw/ l1h1 wkh orz uhdol}dwlrq ri frvw ri vhuylfh surylvlrq1 Vlqfh +5, dqg +8, duh elqglqj
lq htxloleulxp/ dqg +6, dqg +7, duh vodfn/ lqfuhdvlqj ve grhv qrw glvwruw lqfhqwlyh frpsdwlelolw|/ dv
orqj dv ve     v . te 1
       Vlqfh lqfuhdvlqj v lv frvwo| iru wkh djhqf| dqg grhv qrw lqfuhdvh wkh lqyhvwphqw lqfhqwlyh/ zh
nqrz wkdw/ lq dq| uhqhg SIF frqwudfw/ v @ 31 Wkh kljkhvw uhqw wkh djhqf| fdq wkhuhiruh jlyh
wr wkh SIF/ dqg vwloo lqgxfh wuxwkwhoolqj derxw wkh h!flhqf| ri wkh dvvhw lv ve @ te  1 Qrwh wkdw
xqghu wklv uhyhdolqj uhqhg frqwudfw/ wkh SIF*v lqglylgxdo udwlrqdolw| +sduwlflsdwlrq, frqvwudlqw
lv ri frxuvh dozd|v vdwlvhg/ dqg qr dgglwlrqdo wudqvihuv duh uhtxluhg1 Wkh djhqf|*v sd|r iurp
lqfuhdvlqj lqirupdwlrqdo uhqw xs wr vW lv43
                                     e


                          U
                         Y7 +s> vW ,
                                 e       s ^y+te,  te e  vW ` . +4  s, ^y+t ,  t  ` =
                                                              e


+Vxevfulsw L uhihuv wr lqfuhdvhg vxevlg| ve / uhodwlyh wr wkh vwdqgdug fdvh1,
       Krz idu lv wkh djhqf| suhsduhg wr lqfuhdvh uhqw li wkdw lqfuhdvh lqgxfhv lqyhvwphqwB Wkh djhqf|*v
                                                            U
sd|r iurp lqfuhdvhg uhqw vW +li lw lqgxfhv lqyhvwphqw, lv Y7 +sQ > vW ,1 Wkh sd|r iurp zulwlqj wkh
                           e                                         e

orzhvw0uhqw uhyhdolqj frqwudfw +li wkdw grhv qrw lqgxfh lqyhvwphqw, lv Y7 +sB ,1 Li wkh djhqf| fdq
lqgxfh lqyhvwphqw wkdw zd|/ lw zrxog wkhuhiruh zlvk wr lqfuhdvh wkh vxevlg| +lqirupdwlrq uhqw, wr
wkh orz0frvw SIF xs wr

                              sQ    sB                         sQ  sB                        sB
                       vW @
                        e                 ^y+te ,  y+t ,`              ^te e  t  ` .        t =
                                   sQ                             sQ                           sQ

       Wkh lqwxlwlrq iru wklv uhvxow lv vlpsoh= wkh lqirupdwlrq uhqw +zklfk lv sdlg zlwk suredelolw| sQ ,
deryh wkh vwdqgdug lqirupdwlrq uhqw t  +zklfk lv sdlg zlwk suredelolw| sB ,/ lv zruwkzkloh li lw lv
   Zh qhhg qrw frqvlghu plvuhsuhvhqwdwlrq frqwudfwv khuh= lw lv d vwudljkwiruzdug fruroodu| wr ohppd 6 wkdw zlwkrxw
  43


gdpdjh sd|phqwv/ wkh wuxwk0whoolqj frqwudfw lv dozd|v suhihuhg wr d plvuhsuhvhqwdwlrq frqwudfw1

                                                            49
ohvv wkdq/ ru htxdo wr/ wkh h{shfwhg jdlq lq qhw frqvxphu vxusoxv

                                       +sQ  sB , ^y+te ,  y +t , . t   te e ` =

Wkh vdph phwkrg ri surri hpsor|hg deryh vkrzv wkdw

                                                   t      vW  te >
                                                               e


vr wkdw zh nqrz wkdw wkh srlqw wr zklfk wkh djhqf| zrxog zlvk wr lqfuhdvh wkh vxevlg| wr wkh SIF
lv +d, juhdwhu wkdq wkh orzhvw uhqw wkdw lqgxfhv uhyhodwlrq dqg +e, ohvv wkdq wkh kljkhvw uhqw wkdw
vwloo lqgxfhv vhsdudwlrq1 Wklv odvw uhvxow lv vxppdul}hg lq wkh iroorzlqj ohppd=

Ohppd 8       t     vW  te 1
                         e


     Surri1   Lw lv vwudljkwiruzdug wkdw t   vW 1 Zh qhhg wr vkrz wkdw
                                                  e


                                                 y +te ,  y+t ,        te =
Xvlqj wkh e| qrz idploldu phwkrg ri surri= glylglqj e| t / dqg ohwwlqj t                                    $ 3/ zh kdyh
                                                          y  +t ,    e >
zklfk lv wuxh iru doo t5 ^e >  `1
     Wkh surri wkdw vW  te  lv voljkwo| pruh lqyroyhg1 Zh qhhg wr vkrz wkdw
                     e

                   sQ  sB                      sQ  sB                    sB
                           ^y +te ,  y+t ,`          ^te  e  t  ` . t   te 
                          sQ                                sQ                              sQ

ru

                         +sQ  sB , ^y +te ,  y+t ,` . sB te  sQ te  sQ t                        3
djdlq/ glylglqj e| t dqg ohwwlqj t            $ 3/ zh rewdlq
                                                                            sQ
                                                y +t ,    e .                   
                                                                      sQ     sB
zklfk/ vlqfh 3 ?        RQ
                      RQ 3RB   ? 4/ lv wuxh iru doo t     5 ^e >  `1
     Wkh suhfhglqj glvfxvvlrq surpswv rxu qh{w uhvxow=

Sursrvlwlrq 9         Li wkh jryhuqphqw djhqf| fkrrvhv SSS wkhq wkh jryhuqphqw djhqf| zdqwv wr lp0

sohphqw lqyhvwphqwv xs wr dq lqyhvwphqw frvw ri

                               sQ  sB                           sQ     sB                           sB
                         l@              ^y+te ,  y +t ,`                     ^te e  t  ` .        t =
                                  sQ                                   sQ                             sQ


                                                                 4:
      Surri1    Vlqfh zh nqrz wkdw wkh vhuylfh surylghu zloo lqyhvw li/ dqg rqo| li/ l  ve / dqg zh nqrz
wkdw wkh djhqf| lv zloolqj wr lqfuhdvh ve xs wr

                            sQ  sB                            sQ    sB                        sB
                                      ^y+te ,  y+t ,`                   ^te e  t  ` .        t >
                               sQ                                   sQ                          sQ

wkh sursrvlwlrq iroorzv1


616      Wkh Rswlpdo Fkrlfh ri Phfkdqlvp

Zh qrz kdyh d frpsohwh ghvfulswlrq ri lpsohphqwdeoh lqyhvwphqwv xqghu frqyhqwlrqdo surylvlrq
dqg sxeolfsulydwh sduwqhuvklsv1 Lq wklv vhfwlrq/ zh wxuq wr wkh txhvwlrq ri zklfk ri wkhvh phdqv
ri vhuylfh gholyhu| wkh djhqf| zloo fkrrvh1
      Frqvlghu uvw lqyhvwphqwv wkdw fdq eh lqgxfhg erwk xqghu frqyhqwlrqdo sxeolf vhuylfh surylvlrq
dqg xqghu SSS1 Iru lqyhvwphqwv wkdw fdq eh lqgxfhg erwk zkhq wkh djhqf| ex|v wkh dvvhw dqg
zkhq wkh djhqf| ex|v vhuylfhv rqo| +wkdw lv/ iru doo lqyhvwphqw frvwv l  y+te ,  y+t ,  te ,/ vwdwh
rzqhuvkls +zkhq lqyhvwphqw lv lqgxfhg, jlyhv wkh djhqf| dq h{ dqwh h{shfwhg sd|r ri

                          Y +sQ > g,  +sQ
                           A
                                                    sB,l  +4  sQ,g @ Y +sQ > 3,  +sQ  sB ,l
                                                                         A



+wkh exloghu qhhgv wr eh uhlpexuvhg iru wkh h{shfwhg frvw ri lqyhvwphqw dqg wkh h{shfwhg gdpdjh
sd|phqwv,1 Ex|lqj rqo| vhuylfhv jlyhv wkh djhqf| dq h{ dqwh sd|r ri

                            Y7 +sQ > l, @ sQ ^y+te ,  te e
                             U
                                                                     l` . +4  sQ, ^y+t ,  t  ` =

      Wkh djhqf| fkrrvhv wkh vwuxfwxuh wkdw pd{lpl}hv lwv h{ dqwh h{shfwhg sd|r> wkdw lv/ lw fkrrvhv
SSS ryhu frqyhqwlrqdo vhuylfh gholyhu| zkhq44

                                 Y7 +sQ > pd{il> t j,
                                  U
                                                                 Y +sQ> 3,  +sQ  sB,l=
                                                                   A



Wklv ri frxuvh lv mxvw

                                                   sQ                              sQ
                                      l                  pd{il> t j                  t =
                                              sQ    sB                       sQ    sB
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wuxwk0whoolqj frqwudfw lv suhihuuhg wr d plvuhsuhvhqwdwlrq frqwudfw1 Lw lv wkhuhiruh vwudljkwiruzdug
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sdluv +l> sB , vxfk wkdw

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      Surri1    Wkh sursrvlwlrq iroorzv iurp wkh suhfhglqj glvfxvvlrq1
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                                                  t  ? y+te ,  y +t ,  te =


                    Iljxuh 4= lqyhvwphqwv xqghu frqyhqwlrqdo dqg SSS vhuylfh surylvlrq



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wkdw lpsuryh dvvhw txdolw| gudpdwlfdoo| + RQ lv odujh,/ SSS lv rswlpdo1 Wklv lv vwudljkwiruzdug=
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                                                                     53
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lv ohvv frvwo| iru wkh djhqf| vlqfh wkh SIF qhhgv wr rewdlq uhqw dq|zd| lq rughu wr uhyhdo frvw
frqglwlrqv wr wkh djhqf|1 Iru vpdoo lqyhvwphqw frvwv/ wklv +vwdqgdug, uhqw lv vx!flhqw iru wkh SIF
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sd| wkh exloghu vhsdudwho| iru wkh h{shfwhg lqyhvwphqw frvw/ zklfk lv pruh frvwo|1 Iru lqwhuphgldwh
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7     Surmhfwv zlwk Srvlwlyh Vhuylfh Vhw Xs Frvwv

714   Frqyhqwlrqdo Surylvlrq

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                                                     54
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                                         .
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+dqg wkhuhiruh d exlog frqwudfw zlwk gdpdjhv ri vl}h g @ l lv qhfhvvdu|,/ lv

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                                        .



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lqyhvwphqw +dqg wkhuhiruh uhtxluhv }hur gdpdjhv lq wkh exlog frqwudfw, lv

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                                                           55
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                                              .
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                                       l    y+te ,  y+t , . t   te e =

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lqyhvwphqw frvwv ri

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                                                           56
                                                  .
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Sursrvlwlrq ;           Zkhq wkhuh lv d srvlwlyh vhw xs frvw ri vhuylfh surylvlrq/ wkh jryhuqphqw djhqf|

zdqwv wr lpsohphqw lqyhvwphqw xs wr dq lqyhvwphqw frvw ri


                                             l @ y+te ,  y+t , . t     te e =

Ixuwkhupruh/ wkh jryhuqphqw djhqf| lv lqglhuhqw ehwzhhq frqyhqwlrqdo sxeolf vhuylfh surylvlrq

+ex|lqj dvvhwv, dqg SSS vhuylfh surylvlrq +ex|lqj vhuylfhv,1


         Surri1   Wkh sursrvlwlrq iroorzv iurp wkh suhfhglqj glvfxvvlrq1
         Wkh lqwxlwlrq lv wkdw wkh rhu ri d jhqhulf frqwudfw uhyhdov wkdw wkh surmhfw kdv kljk vhw xs
frvwv1 Wkh djhqf| reylrxvo| grhv ehwwhu zlwk d jhqhulf frqwudfw vlqfh lw surwhfwv lw iurp kdylqj wr
jlyh lqirupdwlrq uhqw wr wkh vhuylfh surylghu dqg wkh SIF zkhuhdv d uhqhg frqwudfw zrxog dovr
uhyhdo wkdw wkh surmhfw lv kljk frvwv exw zrxog h{srvh wkh djhqf| wr d orvv wkurxjk lqirupdwlrq
uhqw edvhg rq wkh ohyho ri h!flhqf|1 Vlqfh doo sduwlhv vljq jhqhulf frqwudfwv wkhuh lv qr glhuhqfh lq
h{shfwhg uhwxuqv wr wkh djhqf|1


8         Uhyhdolqj Il{hg Frvwv

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fkdudfwhulvwlf= Zkhqhyhu wkh jryhuqphqw djhqf| kdv d surmhfw wkdw lw nqrzv kdv }hur vhuylfh vhw
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frqwudfw1 Rhulqj d jhqhulf frqwudfw wkhuhiruh lpsolhv wkdw wkh jryhuqphqw djhqf| kdv d surmhfw
zlwk srvlwlyh vhuylfh vhw xs frvw/ f1 Wkh lqwxlwlrq iru wklv uhvxow lv vlpsoh= Li wkh djhqf| rhuv d
surmhfw zlwk srvlwlyh vhuylfh vhw xs frvw dqg wkh vhuylfh surylghu ru SIF grhv qrw kdyh lqirupdwlrq
derxw wkh vhw xs frvw/ wkh djhqf| qhhg rqo| sd| wkh vhuylfh surylghu wkh h{shfwhg frvw +erwk {hg
dqg yduldeoh, ri vhuylfh surylvlrq1 Wkdw lv/ lw fdq zulwh d frqwudfw wkdw lqgxfhv wuxwk0whoolqj e|
wkh vhuylfh surylghu ru SIF zlwkrxw ohdylqj wkh vhuylfh surylghu ru SIF lqirupdwlrq uhqw145 Exw
li wkh vhuylfh vhw xs frvw/ f/ lv odujh/ d jryhuqphqw djhqf| wkdw kdv d surmhfw zlwk }hur vhuylfh
vhw xs frvw kdv dq lqfhqwlyh wr ghyldwh iurp vxfk d srrolqj htxloleulxp= li wkh djhqf| fdq uhyhdo
    45
         Wuxwkwhoolqj frqwudfwv zlwkrxw suh0frqwudfwxdo lqirupdwlrq ri wklv w|sh duh vwxglhg e| Fuìphu dqg Nkdolo +4<<5,1
                                                             57
wkdw wkh vhuylfh vhw xs frvw ri lwv surmhfw lv }hur/ lw qhhg qrw sd| wkh vhuylfh surylghu ru SIF iru
h{shfwhg vhuylfh vhw xs frvwv dw doo1 Lq rxu prgho/ li wkh jryhuqphqw djhqf| kdv d surmhfw zlwk }hur
vhuylfh vhw xs frvw/ lw fdq glvwlqjxlvk lwvhoi e| rhulqj d uhqhg frqwudfw/ dqg wkhuhiruh eulqj derxw
d vhsdudwlqj htxloleulxp1 Krzhyhu/ uhyhdolqj lqirupdwlrq derxw wkh vhw xs frvw lv lwvhoi frvwo| vlqfh
d uhqhg frqwudfw doorzv wkh vhuylfh surylghu ru SIF wr ohduq wkh yduldeoh frvw ri vhuylfh surylvlrq
 dovr/ dqg wkh vhuylfh surylghu ru SIF fdq wkhuhiruh h{wudfw lqirupdwlrq uhqw1 Li wkh vhw0xs frvw

ri vhuylfh surylvlrq lv odujh hqrxjk/ krzhyhu/ zh rewdlq vhsdudwlrq ri w|shv1
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frvw/ fW / vxfk wkdw wkh htxloleulxp lv d vhsdudwlqj htxloleulxp iru doo f juhdwhu wkdq fW dqg glvfxvv
wklv dvvxpswlrq1 Wklv uhvxow lv vwdwhg lq wkh iroorzlqj sursrvlwlrq=

Sursrvlwlrq <    Wkhuh h{lvwv d ohyho ri {hg frvw ri vhuylfh surylvlrq fW vxfk wkdw/ li wkh jryhuqphqw

djhqf| kdv d surmhfw zlwk }hur vhuylfh vhw xs frvw/ lw zloo dozd|v uhyhdo wkdw lqirupdwlrq wr wkh vhuylfh

surylghu ri SIF1 Wkdw lv/ d vhsdudwlqj htxloleulxp h{lvwv1


    Wkh surri lv lq wkh Dsshqgl{1
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vhuylfh vhw xs frvw/ f/ wr wdnh rq dq| +dqg frqfhlydeo| vpdoo, ydoxhv/ jlyhv xv d odujh qxpehu
ri fdvhv> iru vrph frpelqdwlrqv ri l dqg f/ qrq0h{lvwhqfh ri sxuh0vwudwhj| srrolqj ru vhsdudwlqj
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xqghu wkh dvvxpswlrq wkdw f A fW 1


9    Frqfoxvlrq

Zh kdyh vwxglhg d jryhuqphqw djhqf|*v delolw| wr zulwh frqwudfwv derxw sxeolf vhuylfh gholyhu|
dqg2ru dvvhw surfxuhphqw/ zkhq vhuylfhv duh gholyhuhg xvlqj wkdw dvvhw1 Wkh jryhuqphqw djhqf|*v
delolw| wr lpsohphqw lqyhvwphqw lq h!flhqf|0hqkdqfhphqwv e| wkh dvvhw exloghu lv ghwhuplqhg e|
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+wkh frqyhqwlrqdo phfkdqlvp,/ ru zkhwkhu wkh djhqf| frqwudfwv rq vhuylfh surylvlrq rqo| +dv lq wkh

                                                   58
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                                                  59
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